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Analytical formulas for a local volatility model with stochastic rates


  • E. Benhamou
  • E. Gobet
  • M. Miri


This paper presents new approximation formulae for European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models [ Int. J. Theor. Appl. Finance , 2010, 13 (4), 603--634] for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurate approximations with tight estimates of the error terms. This approach can also be used in the case of stochastic dividends or stochastic convenience yields. We finally provide numerical results to illustrate the accuracy with real market data.

Suggested Citation

  • E. Benhamou & E. Gobet & M. Miri, 2012. "Analytical formulas for a local volatility model with stochastic rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 185-198, September.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:2:p:185-198 DOI: 10.1080/14697688.2010.523011

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    References listed on IDEAS

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    Cited by:

    1. Recchioni, M.C. & Sun, Y., 2016. "An explicitly solvable Heston model with stochastic interest rate," European Journal of Operational Research, Elsevier, vol. 249(1), pages 359-377.
    2. Gobet, Emmanuel & Miri, Mohammed, 2014. "Weak approximation of averaged diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 475-504.
    3. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion formulas for European quanto options in a local volatility FX-LIBOR model," Papers 1801.01205,
    4. repec:kap:rqfnac:v:48:y:2017:i:3:d:10.1007_s11156-016-0569-x is not listed on IDEAS
    5. Romain Bompis & Emmanuel Gobet, 2012. "Asymptotic and non asymptotic approximations for option valuation," Post-Print hal-00720650, HAL.
    6. Maria Cristina Recchioni & Yu Sun & Gabriele Tedeschi, 2016. "Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model," Working Papers 2016/23, Economics Department, Universitat Jaume I, Castellón (Spain).

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